Question

A tank holds 128 moles of argon gas (atomic mass = 6.633521

Answer 1

Tank holds 128 moles of argon gas

                          m = 6.633521x10^-26 kg

                          p= 101300 Pa,            T =316 K          A= 6.022x10²³

1. Average speed of argon gas

                              v_ave= sq rt (8RT/ pi M)

                    R= 8.3       M= molar mass

                                       M = A x m / no of mole

                                            = 6.022²³ x 6.633521x10^-26 /128

                                           M= 3.117x10^-4 kg/mole

                  v_ave = sq rt ( 8RT/pi M)

                         = sq rt (( 8 x 8.3 x 316) /(3.14 x 3.117x10^-4))

                              v_ave =4630 m/s

                         The average speed of argon atom =4630 m/s

2. escape velocity of earth = 11200 m/s

                         escape velocity = average velocity

                        v_e = sq rt (8RT/ pi M)

                          8RT / pi M = v_e²

                               T = pi v_e² M / 8R

                                    = 3.14 x 11200² x 3.117x10^-4 /( 8 x 8.3 )

                                  T =1849 K

Escape velocity of earth and average velocity of argon gas are equal at temperature T= 1849 K